We study gravimetry with bosonic trapped atoms in the presence of random spatial inhomogeneity. The errors resulting from a random, shot-to-shot fluctuating spatial inhomogeneity are quantum non-Markovian. We show that in a system with $L>2$ modes (i.e., trapping sites), these errors can be post-corrected using a Bayesian inference. The post-correction is done via in situ measurements of the errors and refining the data-processing according to the measured error. We define an effective Fisher information $F_{\text{eff}}$ for such measurements with a Bayesian post-correction and show that the Cramer-Rao bound for the final precision is $\frac{1}{\sqrt{F_{\text{eff}}}}$ . Exploring the scaling of the effective Fisher information with the number of atoms $N$ , we show that it saturates to a constant when there are too many sources of error and too few modes. That is, with $\ell$ independent sources of error, we show that the effective Fisher information scales as $F_{\text{eff}} \sim \frac{N^2}{a+bN^2}$ for constants $a, b>0$ when the number of modes is small: $L<\ell+2$ , even after maximization over the Hilbert space. With larger number of modes, $L\geq \ell+2$ , we show that the effective Fisher information has a Heisenberg scaling $F_{\text{eff}}= O(N^2)$ when optimized over the Hilbert space. Finally, we study the density of the effective Fisher information in the Hilbert space and show that when $L\geq \ell+2$ , almost any Haar random state has a Heisenberg scaling, i.e., $F_{\text{eff}}=O(N^2)$ . Based on these results, we develop a Loschmidt echo-like experimental sequence for error mitigated gravimetry and gradiometry and discuss potential implementations. Finally, we argue that the effective Fisher information can be interpreted as the Fisher information corresponding to an equivalent non-Hertimitian evolution.We study gravimetry with bosonic trapped atoms in the presence of random spatial inhomogeneity. The errors resulting from a random, shot-to-shot fluctuating spatial inhomogeneity are quantum non-Markovian. We show that in a system with $L>2$ modes (i.e., trapping sites), these errors can be post-corrected using a Bayesian inference. The post-correction is done via in situ measurements of the errors and refining the data-processing according to the measured error. We define an effective Fisher information $F_{\text{eff}}$ for such measurements with a Bayesian post-correction and show that the Cramer-Rao bound for the final precision is $\frac{1}{\sqrt{F_{\text{eff}}}}$. Exploring the scaling of the effective Fisher information with the number of atoms $N$, we show that it saturates to a constant when there are too many sources of error and too few modes. That is, with $\ell$ independent sources of error, we show that the effective Fisher information scales as $F_{\text{eff}} \sim \frac{N^2}{a+bN^2}$ for constants $a, b>0$ when the number of modes is small: $L<\ell+2$, even after maximization over the Hilbert space. With larger number of modes, $L\geq \ell+2$, we show that the effective Fisher information has a Heisenberg scaling $F_{\text{eff}}= O(N^2)$ when optimized over the Hilbert space. Finally, we study the density of the effective Fisher information in the Hilbert space and show that when $L\geq \ell+2$, almost any Haar random state has a Heisenberg scaling, i.e., $F_{\text{eff}}=O(N^2)$. Based on these results, we develop a Loschmidt echo-like experimental sequence for error mitigated gravimetry and gradiometry and discuss potential implementations. Finally, we argue that the effective Fisher information can be interpreted as the Fisher information corresponding to an equivalent non-Hertimitian evolution.

quant-pharXiv:2603.03426Mar 5, 20260 citations

Kinetic Energy and Fisher Information

Ágnes Nagy

Recent advances in computationalApr 21, 20131 citation

Anisotropic activations controlling doublet–quartet spin conversion of linked chromophore-radical molecular qubits in fluid

Yasuhiro Kobori, Yuya Kokado, Kevin Lars Kopp +2 more

Light-energy conversion processes causing alternations in spin multiplicity are attracting attention, but the development of quantum sensing technology applicable to fluid environment such as inside cells has been unexploited. How to achieve efficient energy conversion with controlling spin quantum coherence in a noisy condensed system is challenging. In this study, we investigate the effect of molecular motion on electron spin polarization to control quantum information of three-spin qubits in a fluid environment by using steric effects of organic molecules at room temperature. Using time-resolved electron paramagnetic resonance to observe light-induced generation and transfer of quantum entanglement, we directly observed a photoexcited quartet state generated in a radical-chromophore coupled system and clarified details of the electron spin polarization mechanism including a decoherence effect by activation of anisotropic molecular motion by the steric effects.Light-energy conversion processes causing alternations in spin multiplicity are attracting attention, but the development of quantum sensing technology applicable to fluid environment such as inside cells has been unexploited. How to achieve efficient energy conversion with controlling spin quantum coherence in a noisy condensed system is challenging. In this study, we investigate the effect of molecular motion on electron spin polarization to control quantum information of three-spin qubits in a fluid environment by using steric effects of organic molecules at room temperature. Using time-resolved electron paramagnetic resonance to observe light-induced generation and transfer of quantum entanglement, we directly observed a photoexcited quartet state generated in a radical-chromophore coupled system and clarified details of the electron spin polarization mechanism including a decoherence effect by activation of anisotropic molecular motion by the steric effects.

The Journal of Chemical PhysicsFeb 4, 20255 citations

Phase-space Fisher information

István Hornyák, Ágnes Nagy

Chemical Physics LettersFeb 5, 200732 citations

Fisher Information Measures under Lattice Combined Paul Trap

Precious Ogbonda Amadi, Paphon Pewkhom, Pruet Kalasuwan +3 more

We examine how the informational properties of a confined single ion response in a Paul trap modified by optical-lattice. We focus on the ground and first excited motional states and show that Fisher information, Shannon entropy, and Fisher-Shannon complexity track the effective frequency $ω_{\mathrm{eff}}=ω\sqrt{1-κ}$ of the potential. We show that the Fisher information and Shannon entropy reflect an effective frequency-driven redistribution of information between conjugate spaces. Our results show that the Fisher-Shannon complexity measure remains invariant under effective frequency control. The invariance demonstrates that optical modulation of $κ$ rescales localization, without altering the harmonic structure of the motional states. These results establish a controlled information-theoretic baseline for lattice-assisted Paul traps. Beyond the harmonic limit, retaining the quartic lattice correction introduces non-Gaussian wavefunction features through state-dependent mixing of higher eigenstates, which breaks the mutual compensation between Fisher information and Shannon entropy that sustains the invariant. The departure of $P'$ from its harmonic reference value intensifies with $κ$ and is stronger for the excited state, which confirms that the Fisher-Shannon complexity invariance is a distinctive property of the small-oscillation harmonic regime.We examine how the informational properties of a confined single ion response in a Paul trap modified by optical-lattice. We focus on the ground and first excited motional states and show that Fisher information, Shannon entropy, and Fisher-Shannon complexity track the effective frequency $ω_{\mathrm{eff}}=ω\sqrt{1-κ}$ of the potential. We show that the Fisher information and Shannon entropy reflect an effective frequency-driven redistribution of information between conjugate spaces. Our results show that the Fisher-Shannon complexity measure remains invariant under effective frequency control. The invariance demonstrates that optical modulation of $κ$ rescales localization, without altering the harmonic structure of the motional states. These results establish a controlled information-theoretic baseline for lattice-assisted Paul traps. Beyond the harmonic limit, retaining the quartic lattice correction introduces non-Gaussian wavefunction features through state-dependent mixing of higher eigenstates, which breaks the mutual compensation between Fisher information and Shannon entropy that sustains the invariant. The departure of $P'$ from its harmonic reference value intensifies with $κ$ and is stronger for the excited state, which confirms that the Fisher-Shannon complexity invariance is a distinctive property of the small-oscillation harmonic regime.

quant-pharXiv:2512.14155Scientific ReportsDec 17, 20250 citations

L>2

modes (i.e., trapping sites), these errors can be post-corrected using a Bayesian inference. The post-correction is done via in situ measurements of the errors and refining the data-processing according to the measured error. We define an effective Fisher information

F_{\text{eff}}

for such measurements with a Bayesian post-correction and show that the Cramer-Rao bound for the final precision is

\frac{1}{\sqrt{F_{\text{eff}}}}

. Exploring the scaling of the effective Fisher information with the number of atoms

N

, we show that it saturates to a constant when there are too many sources of error and too few modes. That is, with

\ell

independent sources of error, we show that the effective Fisher information scales as

F_{\text{eff}} \sim \frac{N^2}{a+bN^2}

for constants

a, b>0

when the number of modes is small:

L<\ell+2

, even after maximization over the Hilbert space. With larger number of modes,

L\geq \ell+2

, we show that the effective Fisher information has a Heisenberg scaling

F_{\text{eff}}= O(N^2)

when optimized over the Hilbert space. Finally, we study the density of the effective Fisher information in the Hilbert space and show that when

L\geq \ell+2

, almost any Haar random state has a Heisenberg scaling, i.e.,

F_{\text{eff}}=O(N^2)

. Based on these results, we develop a Loschmidt echo-like experimental sequence for error mitigated gravimetry and gradiometry and discuss potential implementations. Finally, we argue that the effective Fisher information can be interpreted as the Fisher information corresponding to an equivalent non-Hertimitian evolution.

ω_{\mathrm{eff}}=ω\sqrt{1-κ}

of the potential. We show that the Fisher information and Shannon entropy reflect an effective frequency-driven redistribution of information between conjugate spaces. Our results show that the Fisher-Shannon complexity measure remains invariant under effective frequency control. The invariance demonstrates that optical modulation of

κ

rescales localization, without altering the harmonic structure of the motional states. These results establish a controlled information-theoretic baseline for lattice-assisted Paul traps. Beyond the harmonic limit, retaining the quartic lattice correction introduces non-Gaussian wavefunction features through state-dependent mixing of higher eigenstates, which breaks the mutual compensation between Fisher information and Shannon entropy that sustains the invariant. The departure of

P'

from its harmonic reference value intensifies with

κ

and is stronger for the excited state, which confirms that the Fisher-Shannon complexity invariance is a distinctive property of the small-oscillation harmonic regime.